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Issue No. 08 - Aug. (2012 vol. 61)
ISSN: 0018-9340
pp: 1071-1083
G. Paravati , Dipt. di Autom. e Inf. (DAUIN), Politec. di Torino, Torino, Italy
F. Lamberti , Dipt. di Autom. e Inf. (DAUIN), Politec. di Torino, Torino, Italy
F. Gandino , Dipt. di Autom. e Inf. (DAUIN), Politec. di Torino, Torino, Italy
J-C Bajard , LIP6, Univ. Pierre et Marie Curie, Paris, France
P. Montuschi , Dipt. di Autom. e Inf. (DAUIN), Politec. di Torino, Torino, Italy
The modular exponentiation on large numbers is computationally intensive. An effective way for performing this operation consists in using Montgomery exponentiation in the Residue Number System (RNS). This paper presents an algorithmic and architectural study of such exponentiation approach. From the algorithmic point of view, new and state-of-the-art opportunities that come from the reorganization of operations and precomputations are considered. From the architectural perspective, the design opportunities offered by well-known computer arithmetic techniques are studied, with the aim of developing an efficient arithmetic cell architecture. Furthermore, since the use of efficient RNS bases with a low Hamming weight are being considered with ever more interest, four additional cell architectures specifically tailored to these bases are developed and the tradeoff between benefits and drawbacks is carefully explored. An overall comparison among all the considered algorithmic approaches and cell architectures is presented, with the aim of providing the reader with an extensive overview of the Montgomery exponentiation opportunities in RNS.
residue number systems, Hamming weight, architectural study, algorithmic study, montgomery exponentiation, RNS, residue number system, modular exponentiation, computer arithmetic techniques, arithmetic cell architecture, Computer architecture, Microprocessors, Algorithm design and analysis, Computers, Bismuth, Approximation methods, Delay, modular multiplication., RNS, montgomery reduction, modular exponentiation

G. Paravati, F. Lamberti, F. Gandino, J. Bajard and P. Montuschi, "An Algorithmic and Architectural Study on Montgomery Exponentiation in RNS," in IEEE Transactions on Computers, vol. 61, no. , pp. 1071-1083, 2012.
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